institute of aeronautical engineering...x 10-20 20-30 30-40 40-50 50-60 f 11 12.4 21 12 11.8 from...

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous)

Dundigal, Hyderabad-500043

MECHANICAL ENGINEERING

TUTORIAL QUESTION BANK

Course Title STATISTICS FOR MANAGEMENT

Course Code CMBB05

Programme B.Tech

Semester III MBA

Course Type Foundation

Regulation IARE - R18

Course Structure

Theory Practical

Lectures Tutorials Credits Laboratory Credits

4 - 4 - -

Chief Coordinator Ms. G Joseph Mary, Assistant Professor

Course Faculty Ms. G Joseph Mary, Assistant Professor

COURSE OBJECTIVES:

The course should enable the students to:

I Understand the various statistical techniques and solve problems effectively in the statistics.

II Analyze the different types of skewness and know about the coefficient of variations of skewness.

III Understand the application of statistical measures of central tendency and also statistical measures of dispersion.

IV Understand application of ANOVA, other non-parametric test and analyze the recent trends.

V Apply the time series analysis and also trend analysis of data and also know its importance for solving the problems arising.

COURSE OUTCOMES (COs):

CMBB05.01 Recognize the significance, limitations, origin and development of statistics.

CMBB05.02 Acquire the knowledge about different managerial applications of statistics in various fields in

modern times and analyze the use of computers in statistics.

CMBB05.03 Discuss various types of measures of central tendency and measures of dispersion.

CMBB05.04 Analyze the different types of coefficient of skewness and the coefficient of variation.

CMBB05.05 Understand the tabulation and classification of data to draw effective solutions for solving

problems.

CMBB05.06 Demonstrate the diagrammatical and graphical representation of data by using different

Dimensional diagrams.

CMBB05.07 Examine the differences between uni-variate , bi variate and multi variate data.

CMBB05.08 Apply different types of small sample tests and techniques of ANOVA.

CMBB05.09 Analyze correlation analysis and different types of coefficient of correlation.

CMBB05.10 Describe the regression analysis, time series analysis and trend analysis of data.

TUTORIAL QUESTION BANK

UNIT- I

INTRODUCTION TO STATISTICS

Part - A (Short Answer Questions)

S

No

QUESTIONS Blooms

Taxonomy

Level

Course

Outcomes

Course

Outcomes

(COs)

1 Define the term statistics. Remember CO 1 CMBB05.01

2 Differentiate descriptive and inferential statistics. Understand CO 1 CMBB05.01

3 Define Graphical Method? Remember CO 1 CMBB05.02

4 Define bowleys statistics. Remember CO 1 CMBB05.02

5 State whether statistics is a science or art . Remember CO 1 CMBB05.01

6 What is the use of statistics in biology and medical sciences? Remember CO 1 CMBB05.01

7 What is parametric statistics? Remember CO 1 CMBB05.02

8 Write five stages of statistical investigation. Remember CO 1 CMBB05.02

9 Differentiate primary data and secondary data. Remember CO 1 CMBB05.01

10 Give the example for inductive statistics. Remember CO 1 CMBB05.01

11 Define primary data and secondary data. Remember CO 1 CMBB05.02

12 How statistics are used in accountancy? Remember CO 1 CMBB05.02

13 Define experimental methods. Understand CO 1 CMBB05.01

14 Write about descriptive statistics. Understand CO 1 CMBB05.01

15 Discuss how statistics is useful in planning in an organization. Remember CO 1 CMBB05.02

16 Give two examples of graphical and numerical measures? Understand CO 1 CMBB05.02

17 Why presentation of data is important in statistics. Understand CO 1 CMBB05.01

18 Define descriptive statistics. Remember CO 1 CMBB05.01

19 What is the meaning of inferential statistics? Understand CO 1 CMBB05.02

20 Write any two functions of statistics? Remember CO 1 CMBB05.02

Part - B (Long Answer Questions)

1 Define the term statistics and its development. Understand CO 1 CMBB05.01

2 Describe the various definitions of statistics. Understand CO 1 CMBB05.01

3 What are the managerial applications of statistics and give examples for each

field and how it is used?

Understand CO 2 CMBB05.02

4 What are the various functions of statistics? Understand CO 2 CMBB05.02

5 Explain the importance of statistics in management. Understand CO 1 CMBB05.01

6 What are the limitations of statistics and also describe about the stages of

statistical investigation?

Remember CO 1 CMBB05.01

7 Explain the role of computers in present day statistics. Understand CO 2 CMBB05.02

8 Write in detail about the branches of study. Remember CO2 CMBB05.02

9 What are the characteristics features of statistics? Understand CO 1 CMBB05.01

10 Describe how statistics has evolved. Understand CO 1 CMBB05.01

11 Explain orgin and development of statistics? Understand CO 2 CMBB05.02

12 “Statistics is the science of human welfare”comment on this statement Remember CO 2 CMBB05.02

13 Distiguish between statistical methods and statistics. Understand CO 1 CMBB05.01

14 Discuss the scope and significance of the study of statistics. Understand CO 1 CMBB05.01

15 Explain about different managerial applications of statistics in various fields in

modern times and analyze the use of computers in statistics


16. Discuss the significance of statistics and mathematics in the managerial

sciences.


17. What role does business statistics play in the management of business

enterprice?


18. How can statistics be used by managers for taking effective business decisions? Remember CO 2 CMBB05.02

19. Is statistics an all pervading subject?Examine the issue critically. Remember CO 2 CMBB05.02

Part - C (Problem Solving and Critical Thinking Questions)

1 Write about the qualities of a statistician and explain his roles in an

Statistical works.

Understand

CO 1 CMBB05.01

2 Explain about the uses of statistics in different fields. Understand

CO 1 CMBB05.01

3 “Statistical thinking one day be as necessary for effiecient citizenshipas the

ability to read and write”comment on this statement.


4. Which do you feel constitutes a higher form statistical analysis and Why? Understand

CO 1 CMBB05.01

5. To what uses or functions can statistics put? Understand

CO 1 CMBB05.01

6. How do you think eachbe used to solve real world business problems? Remember CO 2 CMBB05.02

UNIT-II

MEASURES OF CENTRAL TENDENCY

Part – A (Short Answer Questions)

1 Define arithmetic mean. Understand

CO 3 CMBB05.03

2 What are the properties of mode? Remember CO 4 CMBB05.04

3 Define range? Write about the bi- model and multi- model concepts. Understand

CO 3 CMBB05.03

4 How actual mean method is calculated? Remember CO 4 CMBB05.04

5 Explain about the skewness. Understand

CO 3 CMBB05.03

6 Describe about the limitations of average. Remember CO 4 CMBB05.04

7 Define dispersion. Explain the properties of good measures of dispersion. Understand

CO 3 CMBB05.03

8 Define mean deviation. Remember CO 4 CMBB05.04

9 Explain about the median and its merits and demerits. Understand

CO 3 CMBB05.03

10 What are the different types of average? Explain how mode is determined graphically with an example.


11 What are the applications of averages? Explain requisites of a good average

Understand

CO 3 CMBB05.03

12 Explain the relationship between mean, median, mode. Remember CO 4 CMBB05.04

13 What is meant by inter quartile range? Understand

CO 3 CMBB05.03

14 Write in detail about the positively skewed distribution. Remember CO 4 CMBB05.04

15 Explain about the geometric mean with example. Understand

CO 3 CMBB05.03

16 Define standard deviation. Remember CO 4 CMBB05.04

17 Define Harmonic mean. Understand

CO 3 CMBB05.03

18 What is the meaning of Quartile? Remember CO 4 CMBB05.04

19 Describe about quartile deviation. Understand

CO 3 CMBB05.03

20 Write about kurtosis? Remember CO 4 CMBB05.04

Part – B (Long Answer Questions)

1 What are the various factors influencing the selection of averages ?state

the applications and limitations of averages?

Understand

CO 3 CMBB05.03

2 What do you mean by dispersion distinguish between measures of central

tendency and dispersion?


3 What do you mean by measures of central tendency what are its objectives and

characteristics? Explain the requisites of good average?

Understand

CO 3 CMBB05.03

4 What is standard deviation? Explain its merits and demerits? what are the

methods available for computing standard deviation for individual observations?


5 Explain the concept of skewness and its different measures of skewness. Understand

CO 3 CMBB05.03

6 Describe the steps involved in calculating standard deviation for continuous

series.


7 calculate the standard deviation and variance from the following data

Daily

wages

10-12 13-15 16-18 19-21 22-24 25-27 28-30

workers 15 14 17 20 23 26 29

Understand

CO 3 CMBB05.03

8 Calculate the mode from the following data

Marks 0-10 10-20 20-30 30-40 40-50

frequency 8 11 26 9 6


9 Find the median and mean deviation of the following data.

Size 0-10 10-20 20-30 30-40 40-50 50-60 60-70

frequency 7 12 18 25 16 14 8

Understand

CO 3 CMBB05.03

10 From the data given below ,calculate karl persons coefficient of skewness

Age 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60

Person 50 70 80 180 150 120 70 50


11 Calculate the lower and upper quartiles ,fifth decile and 30th

percentile

Class 0-5 5-10 10-15 15-20 20-25

Understand

CO 3 CMBB05.03

frequency 7 18 25 30 20

12 Calculate the arithmetic mean, median and mode from the following:

Marks 0-10 10-20 20-30 30-40 40-50 50-60

F 8 10 20 30 25 12


13 Calculate quartile deviation and coefficient of quartile deviation

X 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50

F 4 12 16 22 10 8 6 4

Understand

CO 3 CMBB05.03

14 Find karl pearsoms coefficient of skewness

Wages 5-15 15-25 25-35 35-45 45-55 55-65 65-75

Earners 100 80 75 60 55 20 0


15 Calculate the median Q1,Q3 from the following data

X 8 12 20 25 30 40

F 9 16 28 46 20 10

Understand

CO 3 CMBB05.03

16 What are the objectives of central dispersion of frequency distribution? Understand

CO 3 CMBB05.03

17 Explain utility of measures of dispersion? Remember CO 4 CMBB05.04

18 Discuss the different types of skewness and know about the coefficient

variations of skewness

Understand

CO 3 CMBB05.03

19 Explain karl pearson coeffiect of skewness with examples? Remember CO 4 CMBB05.04

20 Discuss about Bowly’s Coeffiecient of skewness? Understand

CO 3 CMBB05.03

Part - C (Problem Solving and Critical Thinking Questions)

1 Calculate quartile deviation and coefficient of quartile deviation

X 10-20 20-30 30-40 40-50 50-60

F 11 12.4 21 12 11.8

Understand

CO 3 CMBB05.03

2 From the data given below ,calculate Bowley’s coefficient of skewness

Age 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60

Person 50 70 80 180 150 120 70 50


3 Calculate the Mean deviation from the following data

Marks 0-10 10-20 20-30 30-40 40-50

frequency 8 11 26 9 6

Understand

CO 3 CMBB05.03

4 calculate the quartile deviation and variance from the following data

Daily

wages

10-12 13-15 16-18 19-21 22-24 25-27 28-30

workers 15 14 17 20 23 26 29

Understand

CO 3 CMBB05.03

5 Calculate the Geometric mean, median and mode from the following:

Marks 0-10 10-20 20-30 30-40 40-50 50-60

F 8 10 20 30 25 12


MODULE -III

CORRELATION AND REGRESSION


1 Define tabulation. Understand

CO5 CMBB05.05

2 Discuss the Simple Tabulation Remember CO 6 CMBB05.06

3 Explain about the various types of tabulation. Understand

CO 5 CMBB05.05

4 Give an example for complex table. Understand

CO5 CMBB05.05

5 What do you mean by data classification? Remember CO 6 CMBB05.06

6 Describe about the bivariate tabulation and multivariate tabulation. Understand

CO 5 CMBB05.05

7 Write the differences between quantitative and qualitative classification. Understand

CO5 CMBB05.05

8 Write the types of Bar diagram. Remember CO 6 CMBB05.06

9 What do you mean by Percentage Bar Diagram Understand

CO 5 CMBB05.05

10 Define about Sub-divided Bar Diagram Understand

CO5 CMBB05.05

11 Describe about the multiple Bar Diagram. Understand

CO5 CMBB05.05

12 Write about the Pie diagram Remember CO 6 CMBB05.06

13 Describe about the various types of bar diagrams. Understand

CO 5 CMBB05.05

14 What are ogives curves? Understand

CO5 CMBB05.05

15 Explain about the Pie-Chart. Remember CO 6 CMBB05.06

16 Write about the types of diagrams. Understand

CO 5 CMBB05.05

17 Describe about the sub divided bar diagram. Understand

CO5 CMBB05.05

18 Write about the multiple bar diagram. Remember CO 6 CMBB05.06

19 Define Histogram Understand

CO 5 CMBB05.05

20 What is Deviation Bar Diagram?


1 Explain the advantages of graphical presentation and objectives of

Classification?

Understand

CO5 CMBB05.05

2 What is tabulation? Discuss the purpose and methods of tabulation. Remember CO 6 CMBB05.06

3 What is classification? state the differences between classification and

tabulation and explain the types of classification?

Understand

CO 5 CMBB05.05

4 Write about the need and usefulness of diagrammatic representation of

data. describe any two types of diagrams.

Understand

CO5 CMBB05.05

5 Explain the different types of bar diagram with examples. Remember CO 6 CMBB05.06

6 Draw a pie diagram to represent the following data of proposed expenditure by a

state government for the year 2015-16.

ITEMS EXPENDITURE

Agriculture 4200

Industries 1500

Health 1000

Education 500

Understand

CO 5 CMBB05.05

7 Write the types of Bar Diagram Understand

CO5 CMBB05.05

8 Draw a bar diagram for the following data

Years 1990 1991 1992 1993 1994 1995

Data 12 56 45 40 63 12


9 Draw a pie chart from the data

Movies A B C D E

x 6 7 9 10 4

Understand

CO 5 CMBB05.05

10 Draw a multiple bar diagram from the following data

Yr 2001 2002 2003 2004 2005 2006 2007

Export 1000 1400 5000 1200 3900 3800 2500

Import 1200 4000 6900 5000 5900 2000 1400

Understand

CO 5 CMBB05.05

11 Draw sub divided bar diagram from the following data Science 12 13 45 12 Maths 12 13 33 45 Hindi 11 22 61 10

Telugu 12 10 18 14

Understand

CO5 CMBB05.05

12 Represent The following data by sub division bar diagrams:

Year 2006 2007 2008

Gross income 405 480 550

Gross expenditure

(in lakhs)

400 450 500

Net income 5 30 50


13 The following is the distribution of weights (in kgs) of 50 persons

Weight 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90

Persons(nos) 12 8 5 4 5 7 6 3

Understand

CO 5 CMBB05.05

14 Draft an appropriate table to show the following

i. Gender(male,female,transgender)

ii. Three ranks (supervisor,assistants,clerks)

iii. Year 2011,2012,2013,2014 and 2015

iv. Age groups 18-50 years over 50 years

Understand

CO5 CMBB05.05

15 Prepare frequency table and cumulative freaquency table.Having prepared the

table ,


i. The highest marks,the lowest marks and the range.

ii. How many students received marks below 40?

iii. How many students received 75 marks and above?

iv. What percentage of students passed this test,taking 40 marks as the

minimum marks required to pass the test?

16 From the pie chart shown below,prepare a suitable table form to represent data

Understand

CO5 CMBB05.05

17 Represent the data shown in the following table by using suitable graphical

method

Dept Town A Town B

Male Female Total Male Female Total

Tea 40 5 45 25 15 40

Coffee 20 35 55 30 30 60

Total 60 40 100 55 45 100


18 Draw suitable diagram for the following

Expenditure Family A Family B

Monthly Income 30000 36000

Expences food 9000 12000

Clothing 7500 6000

Education 1500 10500

Others 11500 9000

Savings 500 1500

Understand

CO 5 CMBB05.05

19 Represent the following data by using simple bar diagram

Years 1999 2000 2001 2002 2003 2004

Sales 8 8.8 9.2 10.2 7.6 12.5

Understand

CO5 CMBB05.05

20 Explain different types of bar diagrams? Remember CO 6 CMBB05.06

Part – C (Problem Solving and Critical Thinking)

1 Draw less than ogive and more than ogive for the following frequency

distributions

Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70

No of

students

4 8 11 15 12 6 3

Understand

CO5 CMBB05.05

2 The following data shows the number of accidents sustains by 313 drivers of

public utility company over a period of 5 years. Draw the frequency polygon

Accidents 0 1 2 3 4 5 6 7 8

Drivers 80 65 50 39 25 19 7 5 3


3 Draw sub divided bar diagram from the following data Science 18 15 16 20 Maths 12 17 18 21 Hindi 13 16 19 22

Telugu 14 18 20 25

Understand

CO 5 CMBB05.05

4 Represent The following data by sub division bar diagrams:

Year 2009 2010 2011

Understand

CO5 CMBB05.05

19%

24%22%

10%

17%

8%

Merck Sun Pfizer GSK Reddy's Abbot

Gross income 510 520 620

Gross expenditure

(in lakhs)

670 850 700

Net income 25 35 55

5. Draw a pie diagram to represent the following data of proposed expenditure by a

state government for the year 2017-18.

ITEMS EXPENDITURE

Agriculture 7000

Industries 8500

Health 6000

Education 5000

Understand

CO 5 CMBB05.05

6. Represent the following data by using simple bar diagram

Years 2001 2002 2003 2004 2005 2006

Sales 9.2 8. 10.5 12.2 13.5 15.2

Understand

CO 6 CMBB05.06

UNIT -IV

SMALL SAMPLE TESTS

Part – A (Short Answer Questions)

1 Describe about the small sample tests. Understand

CO 7 CMBB05.07

2 Write the types of ANOVA. Remember CO 8 CMBB05.08

3 What do you mean by correlation Understand

CO 7 CMBB05.07

4 Write the Assumptions of Anova. Understand

CO 7 CMBB05.07

5 Explain the Applications of Anova. Remember CO 8 CMBB05.08

6 Describe about the scatter diagram. Understand

CO 7 CMBB05.07

7 Write the formula for paired t distribution. Understand

CO 7 CMBB05.07

8 Define null hypothesis. Remember CO 8 CMBB05.08

9 Define alternative hypothesis. Understand

CO 7 CMBB05.07

10 What is Paired t-test Understand

CO 7 CMBB05.07

11 Write the degrees of freedom of chi square test. Remember CO 8 CMBB05.08

12 Define small sample test and t distribution Understand

CO 7 CMBB05.07

13 Write the uses of Chi-Square Test. Understand

CO 7 CMBB05.07

14 What is Goodness of Fit Remember CO 8 CMBB05.08

15 Define Hypothesis Understand

CO 7 CMBB05.07

16 Write the formula for paired t distribution. Understand

CO 7 CMBB05.07

17 Define ANOVA Remember CO 8 CMBB05.08

18 Explain the properties of student’s t distribution Understand

CO 7 CMBB05.07

19 Explain the properties of correlation distribution Understand

CO 7 CMBB05.07


1 Define small sample test and t distribution. Explain the properties of student’s t

distribution and its applications.

Understand

CO 7 CMBB05.07

2 What is ANOVA? What are its assumptions and applications? Remember CO 8 CMBB05.08

3 What is chi-square? Explain its application. What are chi-square statistics and state its assumptions?

Understand

CO 7 CMBB05.07

4 Define correlation? What are the various methods of correlation? Understand

CO 7 CMBB05.07

5 Explain the Goodness of Fit and Independence? Understand

CO 7 CMBB05.07

6 Calculate spearman’s coefficient of correlation between marks assigned to 10

students by judges X and Y in a certain competitive test as shown below

S.N

o

1 2 3 4 5 6 7 8 9 10

X 52 53 42 60 45 41 37 38 25 27

Y 65 68 43 38 77 48 35 30 25 50


7 Compute the correlation coefficient by Karl pearsons method between x and y

and interpret its valve from the following:

x 3 7 8 9 2 4 7

Understand

CO 7 CMBB05.07

y 7 9 2 1 4 6 9

8 Calculate the t -distribution from the following data:

Persons 1 2 3 4 5 6

Before 13 16 60 30 40 50

After 10 45 58 25 30 44

Understand

CO 7 CMBB05.07

9 200 digits are chosen at random from a set of tables. The frequencies of

digits are as follows, use chi-square test to assess the correctness of hypothesis

that the digits were distributed in equal numbers in the tables from which they

were chosen?

X 0 1 2 3 4 5 6 7 8

F 12 23 23 21 16 25 22 20 21

Understand

CO 7 CMBB05.07

10 Explain the steps for one-way anova with example? Remember CO 8 CMBB05.08

11 Explain the Difference between One way Anova and Two way Anova Understand

CO 7 CMBB05.07

12 Samples of two different company’s bulbs are tested for length of life, and the

following data are obtained,

Particulars COMPANY A COMPANY B

Sample size 8 7

Sample mean 1234 1136

Sample S.D 36 40

Understand

CO 7 CMBB05.07

13 A die is rolled 100 times with the following distribution, at the 0.01 level of

significance, determine whether die is true or uniform

Number 1 2 3 4 5 6

Observed

Frequency

17 14 20 17 17 15


14 Discuss in detail Paired T test? Understand

CO 7 CMBB05.07

15 The mean price of shares of Andhra bank during 2004 was $64.inthe year 2005

the mean price $20 randomly selected days is found to be $84 with S,D of

$4.50.test whether there is significance difference in the price of shares for the

two years at 5% significance level


16 Two different types of drugs A and B were tried on certain patients for increasing

weight.6 persons were given drug A and 8 were drug B.

DrugA 7 10 13 12 4 8 - -

Drug B 12 8 3 18 16 9 8 3

Understand

CO 7 CMBB05.07

17 11 sale excecutive trainees are assigned selling jobs right after their

recruitement.After a fortnight they are withdrawn from their field duties and

given a month training.

Sales (Before training) 23,20,19,21,18,20,18,17,23,16,19

Sales (After training) 24,19,21,18,20,22,20,20,23,20,27

Understand

CO 7 CMBB05.07

18 Test whether A,B,C,D are significantly different

Block A B C D

X 5 9 11 10

Y 4 7 8 10

Z 3 5 8 9


19 Support your answer with appropriate statistical analysis.

a. Do the salesman differ significantly in performamance

b. Is there significant different between seasons

Season Salesmen

A B C D Total

Summer 36 36 21 36 129

Winter 28 29 31 31 119

Monsoon 26 28 29 29 112

Total 90 93 81 96 360

Understand

CO 7 CMBB05.07

20 Three technicians operated 4 machines each produced the following no.of units

Anlyze the data and comment using 5% significance level.

Technician Machine

P Q R S Total

A 12 10 18 16 56

B 13 15 18 12 58

C 10 12 16 14 52

Total 35 37 52 42 166

Understand

CO 7 CMBB05.07


1 Perform a analysis of variance on the data given and interpret the results.use 1%

significance level.

Fertilizers Varieties

A B C

P 55 72 47

Q 64 66 53

R 58 57 74

S 59 57 58

Understand

CO 7 CMBB05.07

2 Sample mean A is 10 with variables of 6.5,9.2,7.5,8.0,10,15,6.2,7.3,4.5,10.8and

Sample mean B is 8 with variables of 8.2,3.5,4.1,6.2,7,4.3,5.4,4.6 on the basis of

data test of significance level?


3 A group of 5 patients treated with medicine A 42,39,48,60,41kgs.second group

of 7 patients weigh 38,42,56,64,68,69,and 62Kgs. Do you agree with the clain od

medicin B increases the weight significantly.

Understand

CO 7 CMBB05.07

4 In an investigation on the machine performance, the following results are

obtained.

No.of units inspected No.of defective

Machine1 375 17

Machine2 450 22

Understand

CO 7 CMBB05.07

5 A survey of 240 families with 4 children each revealed the following

distribution.

Male Births 4 3 2 1 0

No of families 10 55 105 58 12

Test whether the male and female births are equally popular.


6 Samples of students were drawn from two universities and from their weights in

kilograms mean and S.D are calculated and shown below make a large sample

test to the significance of difference between means.

Mean Standard

Deviation

Sample Size

University A 55 10 10

University B 57 15 20

Understand

CO 7 CMBB05.07

7 The measurements of the output of two units have given the following results.

Assuming that both samples have been obtained from the normal populations at

10% significant level, test whether the two populations have the same variance.

Unit- A 14.1 10.1 14.7 13.7 14.0

Unit - B 14.0 14.5 13.7 12.7 14.1

Understand

CO 7 CMBB05.07

8 The nicotine in milligrams of two samples of tobacco were found to be as

follows. Test the hypothesis for the difference between means at 0.05 level.

Sample-A 24 27 26 23 25 -

Sample-B 29 30 30 31 24 36


9 From the following data, find whether there is any significant liking in the habit

of taking soft drinks among the categories of employees.

Soft drinks Clerks Teachers officers

Pepsi 10 25 65

Thumsup 15 30 65

Fanta 50 60 30

Understand

CO 7 CMBB05.07

10 Pumpkins were grown under two experimental conditions. Two random samples

of 11 and 9 pumpkins. the sample standard deviation of their weights as 0.8 and

0.5 respectively. Assuming that the weight distributions are normal, test

hypothesis that the true variances are equal.

Understand

CO 7 CMBB05.07

UNIT -V

REGRESSION ANALYSIS


1 Define Regression Analysis. Understand

CO 9 CMBB05.09

2 Discuss Additive Model of Time series Remember CO 10 CMBB05.10

3 Explain Seasonal Variation in the Series. Understand

CO 10 CMBB05.10

4 Define Multiplicative Model. Understand

CO 7 CMBB05.07

5 Define time series analysis? Write the models of time series analysis Understand

CO 9 CMBB05.09

6 Describe about the components of time series analysis Remember CO 10 CMBB05.10

7 Define trend analysis Understand

CO 10 CMBB05.10

8 Write about the method of semi averages Understand

CO 9 CMBB05.09

9 Define index method. Remember CO 10 CMBB05.10

10 Describe the features of index numbers. Understand

CO 10 CMBB05.10

11 Write the formula for Paashe’s Method Understand

CO 9 CMBB05.09

12 Write the formula for Laspeyress Method Remember CO 10 CMBB05.10

13 Define consumers price index. Understand

CO 10 CMBB05.10

14 Write the formula for Fisher’s Index Method Understand

CO 9 CMBB05.09

15 Write about the two lines of regression. Remember CO 10 CMBB05.10


1 What is regression analysis. Discuss the Properties of regression

coefficient.

Understand

CO 9 CMBB05.09

2 Discuss the Models of Time series with Examples? Remember CO 10 CMBB05.10

3 What do you mean by regression line? What are the two equations of

regression line?

Understand

CO 10 CMBB05.10

4 What are the various methods which can be used for measuring trend

component in time series?

Understand

CO 9 CMBB05.09

5 Define Time Series. What are the various components of time series? Remember CO 10 CMBB05.10

6 Compute two regression equations and also calculate coefficient of correction: X 2 4 6 8

Y 5 10 7 14

Understand

CO 10 CMBB05.10

7 Construct a trend line using the method of semi averages from given

Year 2001 2002 2003 2004 2005 2006 2007

Output 700 900 1100 900 1300 1000 1600

data

Understand

CO 9 CMBB05.09

8 Compute price and quantity index numbers for 1993 with 1991 as base

year from the following:

year P-A Q -A P-B Q-B P- C Q-C

1991 5 10 8 6 6 3

1993 4 12 7 7 5 4


9 Fit a trend line to the following data by the free hand method

Years 2001 2002 2003 2004 2005 2006 2007 2008 2009

Sales 19 22 24 20 23 25 23 26 25

Understand

CO 9 CMBB05.09

10 Using the following data fit a trend line using method of semi averages, Year 1996 1997 1998 1999 2000 2001 2002

Output 700 900 1100 900 1300 1000 1600


11 Use of five early moving average method to calculate trend for the

following data. Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Production 133 248 267 299 321 500 350 450 399 550

Understand

CO 10 CMBB05.10

12 Compute the seasonal index for the following data Understand

CO 9 CMBB05.09

Quarter 2000 2001 2001 2003 2004 2005

I 3.5 3.5 3.5 4.0 4.1 4.2

II 3.9 4.1 3.9 4.6 4.4 4.6

III 3.4 3.7 3.7 3.8 4.2 4.3

IV 3.6 4.8 4.0 4.5 4.5 4.7

13 Use of four early moving average method to calculate trend for the

following data. Year 1999 2000 2001 2002 2003 2004 2005 2006

Output 506 620 1036 673 588 696 1116 738

Understand

CO 9 CMBB05.09

14 Determine the regression equation which best fit to the following data:

x 10 12 13 16 17 20 25

y 10 22 24 27 29 33 37


15 The ranks of 16 students in Mathematics and Statistics are as follows

(1,1),(2,10),(3,3),(4,4),(5,5),(6,7),(7,2),(8,6),(9,8),(10,11),(11,15),(12,9),(13,14),(

14,12),(15,16),(16,13). Calculate the rank correlation coefficient for proficiencies

of this group in mathematics and statistics.

Understand

CO 10 CMBB05.10

16 A sample of 12 fathers and their elder sons gave the following data about their

elder sons. Calculate the coefficient of rank correlation.

Fathers 65 63 67 64 68 62 70 66 68 67 69 71

Sons 68 66 68 65 69 66 68 65 71 67 68 70

Understand

CO 9 CMBB05.09

17 Following are the rank obtained by 10 students in two subjects, Statistics and

Mathematics. To what extent the knowledge of the students in two subjects are

related?

Mathematics 48 33 40 9 16 16 65 24 16 57

Statistics 13 13 24 6 15 4 20 9 6 19

Understand

CO 9 CMBB05.09

18 Give the following data compute multiple coefficient of correlation of X3 on X1

and X2.

X1 3 5 6 8 12 14

X2 16 10 7 4 3 2

X3 90 72 54 42 30 12


19 Find the most likely production corresponding to a rainfall 40 from the following

data:

Rain fall(X) Production(Y)

Average 30 500Kgs

Standard deviation 5 100Kgs

Coefficient of correlation 0.8 -

Understand

CO 10 CMBB05.10

20. The heights of mothers and daughters are given in the following table. From the

two tables of regression estimate the expected average height of daughter when

the height of the mother is 64.5 inches.

Height of the

mother(inches)

62 63 64 64 65 66 68 70

Height of the

daughter(inches)

64 65 61 69 67 68 71 65

Understand

CO 9 CMBB05.09


1 Find coefficient of correlation between X and Y for the following data.

X 10 12 18 24 23 27

Y 13 18 12 25 30 10

2 Ten competitors in a musical test were ranked by the three judges A, B and C in

the following order.

Rank A 1 6 5 10 3 2 4 9 7 8

Rank B 3 5 8 4 7 10 2 1 6 9

Rank C 6 4 9 8 1 2 3 10 5 7

Using rank correlation method, discuss which pair of judges has the nearest

approach to common likings in music.


3. Obtain the rank correlation coefficient for the following data.

X 68 64 75 50 64 80 75 40 55 64

Y 62 58 68 45 81 60 68 48 50 70

Understand

CO 9 CMBB05.09

4. Prove that the coefficient of correlation lies between -1 and 1. Remember CO 10 CMBB05.10

Prepared by: Ms. G Joseph Mary, Assistant Professor HOD, MBA

The ranks of the 15 students in two subjects A and B are given below, the two

numbers within the brackets denoting the ranks of the same student in A and B

respectively.

(1,10), (2,7), (3,2), (4,6), (5,4), (6,8), (7,3), (8,1), (9,11), (10,15), (11,9), (12,5),

(13,14), (14,12), (15,13)

Use Spearman’s formula to find the rank correlation coefficient.

Understand

CO 9 CMBB05.09

5. A panel of two judges P and Q graded seven dramatic performances by

independently awarding marks as follows:

Performance 1 2 3 4 5 6 7

Marks by P 46 42 44 40 43 41 45

Marks by Q 40 38 36 35 39 37 41

The eight performance, which judge Q would not attend, was awarded 37 marks

by judge P. If judge Q had also been present, how many marks would be

expected to have been awarded by him to the eight performance.

Understand

CO 10 CMBB05.10

6. What are the various methods which can be used for measuring trend

component in time series?

Understand

CO 9 CMBB05.09

7. Find the multiple linear regression equation of X1 on X2 and X3 from the data

given below:

X1 2 4 6 8

X2 3 5 7 9

X3 4 6 8 10


8 Calculate the regression equation of Y on X from the data given below, taking

deviations from actual means of X and Y.

Price(Rs.) 10 12 13 12 16 15

Amount

Demanded 40 38 43 45 37 43

Estimate the likely demand when the price is Rs. 20.

Understand

CO 9 CMBB05.09

institute of aeronautical engineering...x 10-20 20-30 30-40 40-50 50-60 f 11 12.4 21 12 11.8 from...

Documents